the idea sounds interesting, there is just one point I'm not sure to
understand exactly in your email: which interface do you want to
provide to the remote user: command-line (CLI) or MI?

It's CLI. I think it is more user-friendly rather than MI.

from my point of view, the CLI would be very convenient, it would
allow the use of Eclipse to navigate the source code (instead of
where/list/up/down), and on the other side control the execution and
everything else from the CLI, which is just very powerful when you
know how to use it.

Exactly, it's one of the points.

Actually, the best situation would be the other way around, control
GDB 'directly' so that ReadLine history/completion is also available!
(I don't thing it would work over the network, would it?)

As I know readline doesn't work well with sockets, but tools like rlwrap
over telnet can be used. It's transparent to user and brings part of
readline features like history, line editing, etc. Though gdb
auto-completion is still a question.